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Journal of Applied Mathematics and Computing

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05-01-2021 | Original Research

Stochastic predator–prey Lévy jump model with Crowley–Martin functional response and stage structure

Author: Jaouad Danane

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021

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Abstract

This paper investigates the dynamics of the stochastic predator–prey model with a Crowley–Martin functional response function driven by Lévy noise. First, the existence, uniqueness and boundedness of a global positive solution is proven. Next, the persfor an optimal conditions. Finally, the theoretical results are reinforced by some numerical simulations. We illustrated the sufficient conditions to classify the dynamics of the stochastic predator–prey model.

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Tripathi, J.P., Tyagi, S., Abbas, S.: Global analysis of a delayed density dependent predator–prey model with Crowley–Martin functional response. Commun. Nonlinear Sci. Numer. Simul. 30, 45–69 (2016)MathSciNetCrossRef

Meng, X.Y., Huo, H.F., Xiang, H., Yin, Q.Y.: Stability in a predator–prey model with Crowley–Martin function and stage structure for prey. Appl. Math. Comput. 232, 810–819 (2014)MathSciNetMATH

Liu, Q., Jiang, D.Q., Hayat, T., Alsaedi, A.: Dynamics of a stochastic predator-prey model with stage structure for predator and Holling type II functional response. J. Nonlinear Sci. 28, 1151–1187 (2018)MathSciNetCrossRef

Lotka, A.: Elements of Mathematical Biology. Dover Publications, New York (1956)MATH

Fay, T.H., Greeff, J.C.: Lion, wildebeest and zebra: a predator–prey model. Ecol. Modell. 196(1–2), 237–244 (2006)CrossRef

Spencer, P.D., Collie, J.S.: A simple predator–prey model of exploited marine fish populations incorporating alternative prey. ICES J. Mar. Sci. 53(3), 615–628 (1996)CrossRef

Mukherjee, D.: Persistence and bifurcation analysis on a predator–prey system of Holling type. Esaim Math. Model. Numer. Anal. 37, 339–344 (2003)MathSciNetCrossRef

Liu, Z.J., Zhong, S.M.: Permanence and extinction analysis for a delayed periodic predator-prey system with Holling type II response function and diffusion. Appl. Math. Comput. 216, 3002–3015 (2010)MathSciNetMATH

Zhang, Z., Yang, H., Fu, M.: Hopf bifurcation in a predator-prey system with Holling type III functional response and time delays. J. Appl. Math. Comput. 44, 337–356 (2014)MathSciNetCrossRef

10.

Upadhyay, R.K., Naji, R.K.: Dynamics of a three species food chain model with Crowley–Martin type functional response. Chaos Solitons Fractals 42, 1337–1346 (2009)MathSciNetCrossRef

11.

Cui, J., Takeuchi, Y.: Permanence, extinction and periodic solution of predator-prey system with Beddington–DeAngelis functional response. J. Math. Anal. Appl. 317, 464–474 (2006)MathSciNetCrossRef

12.

Tripathi, J.P., Abbas, S., Thakur, M.: Dynamical analysis of a prey-predator model with Beddington–DeAngelis type function response incorporating a prey refuge. Nonlinear Dyn. 80, 177–196 (2015)MathSciNetCrossRef

13.

Wang, K., Zhu, Y.L.: Permanence and global asymptotic stability of a delayed predator-prey model with Hassell-Varley type functional response. Bull. Iran. Math. Soc. 94, 1–14 (2013)

14.

Wang, W., Chen, L.: A predator–prey system with stage-structure for predator. Comput. Math. Appl. 33, 83–91 (1997)MathSciNetCrossRef

15.

Chen, Y., Song, C.: Stability and Hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay. Chaos Solitons Fractals 38, 1104–1114 (2008)MathSciNetCrossRef

16.

Yang, W., Li, X., Bai, Z.: Permanence of periodic Holling type-IV predator–prey system with stage structure for prey. Math. Comput. Model. 48, 677–684 (2008)MathSciNetCrossRef

17.

Huang, C.Y., Zhao, M., Zhao, L.C.: Permanence of periodic predator–prey system with two predators and stage structure for prey. Nonlinear Anal. Real World Appl. 11(1), 503–514 (2010)MathSciNetCrossRef

18.

Meng, X.Y., Huo, H.F., Xiang, H., Yin, Q.Y.: Stability in a predator–prey model with Crowley–Martin function and stage structure for prey. Appl. Math. Comput. 232, 810–819 (2014)MathSciNetMATH

19.

Sun, X.K., Huo, H.F., Xiang, H.: Bifurcation and stability analysis in predator–prey model with a stage-structure for predator. Nonlinear Dyn. 58, 497–513 (2009)MathSciNetCrossRef

20.

Xu, R.: Global dynamics of a predator–prey model with time delay and stage structure for the prey. Nonlinear Anal. Real World Appl. 12, 2151–2162 (2011)MathSciNetCrossRef

21.

Xu, C., Ren, G., Yu, Y.: Extinction analysis of stochastic predator–prey system with stage structure and Crowley–Martin functional response. Entropy 21(3), 252 (2019)MathSciNetCrossRef

22.

Liu, Q., Jiang, D., Hayat, T., Alsaedi, A.: Dynamics of a stochastic predator–prey model with stage structure for predator and Holling type II functional response. J. Nonlinear Sci. 28(3), 1151–1187 (2018)MathSciNetCrossRef

23.

Choo, S., Kim, Y.H.: Global stability in stochastic difference equations for predator–prey models. J. Comput. Anal. Appl. 23(1) (2017)

24.

Yang, L., Zhong, S.: Global stability of a stage-structured predator-prey model with stochastic perturbation. Discrete Dyn. Nat. Soc. (2014)

25.

Zhao, S., Song, M.: A stochastic predator–prey system with stage structure for predator. Abstr. Appl. Anal. (2014)

26.

Zhang, X., Li, W., Liu, M., Wang, K.: Dynamics of a stochastic Holling II one-predator two-prey system with jumps. Phys. A Stat. Mech. Appl. 421, 571–582 (2015)MathSciNetCrossRef

27.

Liu, Q., Chen, Q.M.: Analysis of a stochastic delay predator–prey system with jumps in a polluted environment. Appl. Math. Comput. 242, 90–100 (2014)MathSciNetMATH

28.

Liu, M., Bai, C., Deng, M., Du, B.: Analysis of stochastic two-prey one-predator model with Lévy jumps. Phys. A Stat. Mech. Appl. 445, 176–188 (2016)CrossRef

29.

Zhao, Y., Yuan, S.: Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps. Chaos Solitons Fractals 85, 98–109 (2016)MathSciNetCrossRef

30.

Wu, J.: Stability of a three-species stochastic delay predator–prey system with Lévy noise. Phys. A Stat. Mech. Appl. 502, 492–505 (2018)CrossRef

31.

Zou, X., Wang, K.: Numerical simulations and modeling for stochastic biological systems with jumps. Commun. Nonlinear Sci. Numer. Simulat 19, 1557–1568 (2014)MathSciNetCrossRef

Title: Stochastic predator–prey Lévy jump model with Crowley–Martin functional response and stage structure
Author: Jaouad Danane
Publication date: 05-01-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2021
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-020-01490-w

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